where the prime denotes now the derivative with respect to \(\xi \) .
In a second step, as suggested in [1]}, we take advantage of the autonomous character of the equation to reduce its order through the substitution \(\eta ^{\prime } = -F^{1/2}\) .
In terms of this function \(F\) , the interface curvature becomes \(\eta ^{\prime \prime } = \frac{1}{2}\mathrm {d}F/\mathrm {d}\eta \)  and equation (REF ) turns into
\(\frac{\mathrm {d}^2F}{\mathrm {d}\eta ^2} = \frac{6\left(\eta -1\right)}{\eta ^3 F^{1/2}}.\) 
